Mathematics

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13 pages, 2489 KiB

Open AccessArticle

Exploring the Impact of Nonlinearities in Police Recruitment and Criminal Capture Rates: A Population Dynamics Approach

by Tichaona Chikore, Farai Nyabadza and K. A. Jane White

Mathematics 2023, 11(7), 1669; https://doi.org/10.3390/math11071669 - 30 Mar 2023

Cited by 2 | Viewed by 1280

The interplay between criminal activity and crime control/prevention measures is inherently dynamic. This paper presents a simple nonlinear dynamical system in which criminal activity levels are coupled to policing effort. Through the process of non-dimensionalisation and sensitivity analysis, policing efficiency and the responsiveness [...] Read more.

The interplay between criminal activity and crime control/prevention measures is inherently dynamic. This paper presents a simple nonlinear dynamical system in which criminal activity levels are coupled to policing effort. Through the process of non-dimensionalisation and sensitivity analysis, policing efficiency and the responsiveness of policing effort are identified as key parameter groupings. An analysis of the system shows that bi-stability is a feature of the dynamics. When there is no feedback between criminal activity and police recruitment, a saddle-node bifurcation occurs and threshold levels of criminal activity are required for the activity to be maintained. When feedback is permitted, we also find a backward bifurcation and criminal activity can be contained for policing efficiency below its threshold level. We demonstrate proof of concept for how the model might be used as a predictive tool with real data. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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14 pages, 3457 KiB

Open AccessArticle

Analysis and Optimal Control of the Tungro Virus Disease Spread Model in Rice Plants by Considering the Characteristics of the Virus, Roguing, and Pesticides

by Rika Amelia, Nursanti Anggriani, Asep K. Supriatna and Noor Istifadah

Mathematics 2023, 11(5), 1151; https://doi.org/10.3390/math11051151 - 25 Feb 2023

Viewed by 1591

Abstract

Farmers have an essential role in maintaining food security. One of the food crops that occupies a high position in Indonesia is rice. However, farmers often experience problems when cultivating rice plants, one of which is affected by the tungro virus disease in [...] Read more.

Farmers have an essential role in maintaining food security. One of the food crops that occupies a high position in Indonesia is rice. However, farmers often experience problems when cultivating rice plants, one of which is affected by the tungro virus disease in rice plants. The spread of the disease can be controlled by the roguing process and applying pesticides. In this study, an analysis of the model of the spread of tungro virus disease in rice plants took into account the characteristics of the rice tungro spherical virus (RTSV) and rice tungro bacilliform virus (RTBV), as well as control in the form of roguing processes and application of pesticides. The analysis carried out was in the form of dynamic analysis, sensitivity analysis, and optimal control. In addition, numerical simulations were also carried out to describe the results of the analysis. The results showed that the roguing process and the application of pesticides could control the spread of the tungro virus disease. The application is sufficient, at as much as 75%. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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21 pages, 628 KiB

Open AccessArticle

Unfolding the Transmission Dynamics of Monkeypox Virus: An Epidemiological Modelling Analysis

by Mohammed M. Al-Shomrani, Salihu S. Musa and Abdullahi Yusuf

Mathematics 2023, 11(5), 1121; https://doi.org/10.3390/math11051121 - 23 Feb 2023

Cited by 8 | Viewed by 1658

Abstract

Monkeypox (mpox) is a zoonotic viral disease that has caused recurring outbreaks in West Africa. The current global mpox virus (mpoxv) epidemic in endemic and non-endemic areas has seriously threatened public health. In this study, we design an SEIR-based deterministic model that considers [...] Read more.

Monkeypox (mpox) is a zoonotic viral disease that has caused recurring outbreaks in West Africa. The current global mpox virus (mpoxv) epidemic in endemic and non-endemic areas has seriously threatened public health. In this study, we design an SEIR-based deterministic model that considers prodromal stage, differential infectivity, and hospitalisation to investigate the transmission behaviour of mpoxv, which could help enhance control interventions. The model is theoretically analyzed by computing essential epidemiological quantities/dynamics, such as the basic reproduction number, which estimates the number of secondary infections caused by a typical primary case in an entirely susceptible community. Stability of the model’s equilibrium states is examined to evaluate the transmission potential of the mpoxv. Furthermore, partial rank correlation coefficient was adopted for sensitivity analysis to determine the top-rank model’s parameters for controlling the spread of mpoxv. Moreover, numerical simulations and model predictions are performed and are used to evaluate the influence of some crucial model parameters that help in strengthening the prevention and control of mpoxv infection. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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18 pages, 6467 KiB

Open AccessArticle

Analysis of Spatiotemporal Transmission Characteristics of African Swine Fever (ASF) in Mainland China

by Xin Pei, Mingtao Li, Jianghong Hu, Juan Zhang and Zhen Jin

Mathematics 2022, 10(24), 4709; https://doi.org/10.3390/math10244709 - 12 Dec 2022

Cited by 2 | Viewed by 1293

Abstract

In view of the rapid spread of African swine fever in Mainland China from 2018 to 2019, we used spatiotemporal statistical analysis methods to study the spatiotemporal transmission features of African swine fever. The results reveal that the hot spots of African swine [...] Read more.

In view of the rapid spread of African swine fever in Mainland China from 2018 to 2019, we used spatiotemporal statistical analysis methods to study the spatiotemporal transmission features of African swine fever. The results reveal that the hot spots of African swine fever were concentrated in some cities in Northeast and Southwest China. Seven spatiotemporal clusters of African swine fever were identified, and the most likely spatiotemporal cluster was located in the Buyi and Miao Autonomous Prefecture of QianNan in Guizhou Province, and the cluster date was from 19 June to 25 June 2019. The first secondary cluster covered five cities (Shenyang, Yingkou, Panjin, Anshan, and Liaoyang) in Liaoning Province from 1 August to 10 October 2018. In addition, from the global and local transmission direction and speed of African swine fever in Mainland China, the spatial transmission speed of ASF was found to be slow from August to October 2018, and fast from February to March 2019. Lastly, the global and local isolation and exposure of sites infected with ASF were calculated in Mainland China to reveal the infection risk of different susceptible sites and time periods. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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21 pages, 1325 KiB

Open AccessArticle

Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19

by Slavi Georgiev and Lubin Vulkov

Mathematics 2022, 10(22), 4247; https://doi.org/10.3390/math10224247 - 13 Nov 2022

Cited by 7 | Viewed by 1184

Abstract

In the present work, a fractional temporal SIR model is considered. The total population is divided into three compartments—susceptible, infected and removed individuals. It generalizes the classical SIR model and consists of three coupled time-fractional ordinary differential equations (ODEs). The fractional derivative is [...] Read more.

In the present work, a fractional temporal SIR model is considered. The total population is divided into three compartments—susceptible, infected and removed individuals. It generalizes the classical SIR model and consists of three coupled time-fractional ordinary differential equations (ODEs). The fractional derivative is introduced to account for the subdiffusion process of confirmed, cured and deceased people dynamics. Although relatively basic, the model is robust and captures the real dynamics, helped by the memory property of the fractional system. In the paper, the issue of an adequate model reconstruction is addressed, and a coefficient identification inverse problem is solved; in particular, the transition and recovering rates, varying in time, are recovered. A least-squares cost functional is minimized for solving the problem. The time-dependent parameters are reconstructed with an iterative predictor–corrector algorithm. Its application is demonstrated via tests with synthetic and real data. What is more, an approach for economic impact assessment is proposed. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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16 pages, 1888 KiB

Open AccessArticle

Infection Eradication Criterion in a General Epidemic Model with Logistic Growth, Quarantine Strategy, Media Intrusion, and Quadratic Perturbation

by Yassine Sabbar, Mehmet Yavuz and Fatma Özköse

Mathematics 2022, 10(22), 4213; https://doi.org/10.3390/math10224213 - 11 Nov 2022

Cited by 10 | Viewed by 1257

Abstract

This article explores and highlights the effect of stochasticity on the extinction behavior of a disease in a general epidemic model. Specifically, we consider a sophisticated dynamical model that combines logistic growth, quarantine strategy, media intrusion, and quadratic noise. The amalgamation of all [...] Read more.

This article explores and highlights the effect of stochasticity on the extinction behavior of a disease in a general epidemic model. Specifically, we consider a sophisticated dynamical model that combines logistic growth, quarantine strategy, media intrusion, and quadratic noise. The amalgamation of all these hypotheses makes our model more practical and realistic. By adopting new analytical techniques, we provide a sharp criterion for disease eradication. The theoretical results show that the extinction criterion of our general perturbed model is mainly determined by the parameters closely related to the linear and quadratic perturbations as well as other deterministic parameters of the system. In order to clearly show the strength of our new result in a practical way, we perform numerical examples using the case of herpes simplex virus (HSV) in the USA. We conclude that a great amount of quadratic noise minimizes the period of HSV and affects its eradication time. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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23 pages, 1962 KiB

Open AccessArticle

Effects of Random Environmental Perturbation on the Dynamics of a Nutrient–Phytoplankton–Zooplankton Model with Nutrient Recycling

by Lifan Chen, Xingwang Yu and Sanling Yuan

Mathematics 2022, 10(20), 3783; https://doi.org/10.3390/math10203783 - 13 Oct 2022

Cited by 1 | Viewed by 1183

Abstract

A stochastic nutrient–phytoplankton–zooplankton model with instantaneous nutrient recycling is proposed and analyzed in this paper. When the nutrient uptake function and the grazing function are linear and the ingested phytoplankton is completely absorbed by the zooplankton, we establish two stochastic thresholds [...] Read more.

A stochastic nutrient–phytoplankton–zooplankton model with instantaneous nutrient recycling is proposed and analyzed in this paper. When the nutrient uptake function and the grazing function are linear and the ingested phytoplankton is completely absorbed by the zooplankton, we establish two stochastic thresholds

R_{0}^{S}

and

R_{1}^{S}

, which completely determine the persistence and extinction of the plankton. That is, if

R_{0}^{S} < 1

, both the phytoplankton and the zooplankton eventually are eliminated; if

R_{0}^{S} > 1

and

R_{1}^{S} < 1

, the phytoplankton is persistent in mean but the zooplankton is extinct; while for

R_{1}^{S} > 1

, the entire system is persistent in mean. Furthermore, sufficient criteria for the existence of ergodic stationary distribution of the model are obtained and the persistent levels of the plankton are estimated. Numeric simulations are carried out to illustrate the theoretical results and to conclude our study. Our results suggest that environmental noise may cause the local bloom of phytoplankton, which surprisingly can be used to explain the formation of algal blooms to some extent. Moreover, we find that the nonlinear nutrient uptake function and grazing function may take credit for the periodic succession of blooms regardless of whether they are in the absence or presence of the environmental noises. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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26 pages, 1257 KiB

Open AccessArticle

A Mathematical Model for Ovine Brucellosis during Dynamic Transportation of Sheep, and Its Applications in Jalaid Banner and Ulanhot City

by Jiaming Guo, Xiaofeng Luo, Juan Zhang and Mingtao Li

Mathematics 2022, 10(19), 3436; https://doi.org/10.3390/math10193436 - 21 Sep 2022

Cited by 1 | Viewed by 1316

Abstract

Brucellosis a the serious infectious disease in Hinggan League. Research has demonstrated that a large amount of transportation is one of the main reasons for so many cases. However, the specific transmission mechanism of brucellosis is not clear. In this paper, we utilize [...] Read more.

Brucellosis a the serious infectious disease in Hinggan League. Research has demonstrated that a large amount of transportation is one of the main reasons for so many cases. However, the specific transmission mechanism of brucellosis is not clear. In this paper, we utilize a multi-patch model to study the effect of the transportation of sheep on the spread of brucellosis in Hinggan League. Theoretically, we prove the global stability of the disease-free equilibrium and the uniform persistence of the endemic equilibrium. In a practical application, we apply the model to investigate the spread of brucellosis in Ulanhot city and Jalaid Banner, which are geographically adjacent in Hinggan League. The strains carried by humans are B.melitensis bv.1 and B.melitensis bv.3. We use the two-patch model to fit reported brucellosis cases data of two places by Markov Chain Monte Carlo (MCMC) simulations. It is found that the global basic reproduction number

R_{0}

is larger than 1, but the isolated basic reproduction numbers in Ulanhot city and Jalaid Banner are both less than 1. This indicates that the prevalence of brucellosis may be caused by the transportation of sheep. Sensitivity analysis of parameters on

R_{0}

shows that it is the most effective means to control the transportation of sheep from Jalaid to Ulanhot on preventing brucellosis. Moreover, we also discover that improving vaccine efficiency is an effective method compared with strengthening the vaccination coverage rate and improving the detection rate of sheep with brucellosis. Our dynamic behavior analysis of the two-patch model can provide a reference for the dynamic behavior analysis of the n-patch model, and our results provide a guide for how to control brucellosis based on transportation. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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28 pages, 509 KiB

Open AccessArticle

Effects of Media Coverage on Global Stability Analysis and Optimal Control of an Age-Structured Epidemic Model with Multi-Staged Progression

by Chao Liu, Peng Chen, Qiyu Jia and Lora Cheung

Mathematics 2022, 10(15), 2712; https://doi.org/10.3390/math10152712 - 1 Aug 2022

Cited by 1 | Viewed by 1400

Abstract

In this paper, a hybrid SEIAM model for infectious disease with a continuous age structure is established, where combined dynamic effects of media coverage and multi-staged infected progression on threshold dynamics are discussed. Sufficient conditions for uniform persistence of the solution are studied [...] Read more.

In this paper, a hybrid SEIAM model for infectious disease with a continuous age structure is established, where combined dynamic effects of media coverage and multi-staged infected progression on threshold dynamics are discussed. Sufficient conditions for uniform persistence of the solution are studied by using the basic reproduction number. By constructing appropriate Lyapunov functions, the global stability analysis of endemic equilibrium is investigated based on Lyapunov–LaSalle’s stability theorem. In order to minimize costs incurred due to applied controls and infectious disease burden, an optimal cost-effective control strategy associated with disease treatment and media coverage is discussed. Numerical simulations are carried out to show consistency with theoretical analysis. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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24 pages, 590 KiB

Open AccessArticle

Optimal Breeding Strategy for Livestock with a Dynamic Price

by Leishi Wang, Mingtao Li, Xin Pei and Juan Zhang

Mathematics 2022, 10(10), 1732; https://doi.org/10.3390/math10101732 - 18 May 2022

Cited by 2 | Viewed by 1378

Abstract

China’s livestock output has been growing, but domestic livestock products such as beef, mutton and pork have been unable to meet domestic consumers’ demands. The imbalance between supply and demand causes unstable livestock prices and affects profits on livestock. Therefore, the purpose of [...] Read more.

China’s livestock output has been growing, but domestic livestock products such as beef, mutton and pork have been unable to meet domestic consumers’ demands. The imbalance between supply and demand causes unstable livestock prices and affects profits on livestock. Therefore, the purpose of this paper is to provide the optimal breeding strategy for livestock farmers to maximize profits and adjust the balance between supply and demand. Firstly, when the price changes, livestock farmers will respond in two ways: by not adjusting the scale of livestock with the price or adjusting the scale with the price. Therefore, combining the model of price and the behavior of livestock farmers, two livestock breeding models were established. Secondly, we proposed four optimal breeding strategies based on the previously studied models and the main research method is Pontryagin’s Maximum Principle. Optimal breeding strategies are achieved by controlling the growth and output of livestock. Further, their existence was verified. Finally, we simulated two situations and found the most suitable strategy for both situations by comparing profits of four strategies. From that, we obtained several conclusions: The optimal strategy under constant prices is not always reasonable. The effect of price on livestock can promote a faster balance. To get more profits, the livestock farmers should adjust the farm’s productivity reasonably. It is necessary to calculate the optimal strategy results under different behaviors. Full article

(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)

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